We consider Markov logic networks and relational logistic regression as two fundamental representation formalisms in statistical relational artificial intelligence that use weighted formulas in their specification. However, Markov logic networks are based on undirected graphs, while relational logistic regression is based on directed acyclic graphs. We show that when scaling the weight parameters with the domain size, the asymptotic behaviour of a relational logistic regression model is transparently controlled by the parameters, and we supply an algorithm to compute asymptotic probabilities. We also show using two examples that this is not true for Markov logic networks. We also discuss using several examples, mainly from the literature, how the application context can help the user to decide when such scaling is appropriate and when using the raw unscaled parameters might be preferable. We highlight random sampling as a particularly promising area of application for scaled models and expound possible avenues for further research.

翻译：我们考虑马尔可夫逻辑网络和关系逻辑回归作为统计关系人工智能中的两种基本表示形式，这两种形式在其规范中均使用加权公式。然而，马尔可夫逻辑网络基于无向图，而关系逻辑回归基于有向无环图。我们证明，当权重参数随领域大小进行缩放时，关系逻辑回归模型的渐近行为由参数透明地控制，并给出了一种计算渐近概率的算法。我们还通过两个实例表明，这一性质对于马尔可夫逻辑网络并不成立。此外，我们通过多个（主要来自文献的）实例讨论应用场景如何帮助用户判断何时适宜进行此类缩放，以及何时更宜使用原始未缩放的参数。我们特别指出随机采样是缩放模型极具前景的应用领域，并探讨了未来可能的研究方向。